But the new death toll is only an approximation, not a concrete list of names, Rossello said.

Moving forward, he said, officials will continue to investigate deaths from the storm and refine the official tally.

"This number can change," he said. "It could be less, it could be more, as time passes."

It could take months or years, he said, to come up with a complete list of storm-related deaths.

"We are using the best science available ... to be able to give a sense of closure to all of this," he said. "The truth is there is a lot of work to do."

The official toll matters in part because families of those who died in the aftermath of the storm are eligible to have some funeral expenses covered by the US government. Experts say higher death tolls drive more disaster aid. And knowing precisely how and why people died can help authorities prevent future hurricane-related deaths.

A key question: Will this new figure -- stemming from a study conducted at the request of Puerto Rican officials -- provide any closure to families that have long argued their loved ones died because of the storm but hadn't received any official acknowledgment?

A new study

Researchers from George Washington University released a study earlier Tuesday, calculating excess deaths that occurred in the US commonwealth between September 2017 and February 2018.

The study, commissioned after the September 2017 storm, followed a number of others like it.

And recently, the Puerto Rican government had quietly admitted the official toll was higher than its December 2017 tally. In a report to Congress earlier this month, the US commonwealth said documents show that 1,427 more deaths occurred in the four months after the storm than "normal," compared with deaths that occurred the previous four years.

But the latest estimate was even higher.

San Juan Mayor Carmen Yulin Cruz blamed President Donald Trump, the federal government and Puerto Rican officials for failing to provide adequate assistance in the aftermath of the storm.

"It's 2,975 people, and they're still calling it an estimate -- 2,975 people that will never see the light of day, and many of them died because of what was done by the administration and that was silently approved by most of the political class in Puerto Rico," Cruz told CNN on Wednesday.

"The administration killed the Puerto Ricans with neglect," she added. "The Trump administration led us to believe they were helping when they weren't up to par, and they didn't allow other countries to help us. ... Shame on President Trump."

White House press secretary Sarah Sanders said Trump "remains proud of all of the work the Federal family undertook to help our fellow citizens in Puerto Rico," according to a statement issued after Tuesday's release of the new death toll estimate.

To that, Cruz asked, "What is there to be proud of? 2,970 dead. Is that what he's proud of?"

Researchers behind George Washington University's study said they felt they were able to provide a more accurate estimate because they took into account additional factors such as migration.

"I do think this study helps to validate that sense that many people had that there were just too many deaths," said Lynn Goldman, dean of the university's Milken Institute School of Public Health.

But she also stressed that Tuesday's report marks only the first phase of the study.

"In the next phase, we would like to dig down deeper into that number to understand among all the deaths that occurred, which of them were related to Maria, which of them would not have occurred if it hadn't been for the storm? We're not able to say that now," Goldman said.

She acknowledged that a complete list may never be possible.

"At the end of the day," she said, "we may never be able to fully identify all those 2,975 people."

'We are not going to revive them'

With many different estimates emerging, it's hard to know whom to believe, said Lourdes Rodriguez, whose father, Natalio, died in January.

"This is up and down numbers. No one knows how or from what (source) is the real number," Rodriguez said. "Due to the island being shut down, there was no way of knowing anything for a week or week and a half after the event."

Natalio Rodriguez's death hasn't been officially classified as related to the storm, but his family believes Maria was to blame. He died after the generator that was running his breathing machine ran out of gas.

And no study, Lourdes Rodriguez said, can make up for what she and so many others lost.

"We are not going to revive them, unfortunately. We just have to be prepared or get prepared for the next event," Rodriguez said. "September is one of the hottest months of the year, and you see people going to the beach and living in la-la land, as if nothing is going to come."

Governor: 'I made mistakes'

The George Washington University study also found that the risk of dying as a result of the storm was the highest for people living in Puerto Rico's poorest municipalities, and that older, male Puerto Ricans had a notably higher risk of death after Maria.

In addition, researchers looked at how storm-related deaths were certified, and they analyzed communication about deaths after the disaster.

Among the study's conclusions: Officials did nothing to respond to public criticisms and concerns about political motivations that surged when the official tally of deaths jumped from 16 to 34 shortly after Trump visited and praised how low the storm's death toll had been.

The governor admitted Tuesday that he'd made mistakes in handling the situation.

"I agree I made mistakes. I agree on that. ... This could have been done differently. I recognize all that," he said. "However, I reject the notion that this was somehow connected to any political consideration. My only consideration is the well-being of the people of Puerto Rico. My only consideration was getting the best available information and the truth out there."

Rossello said he'd signed an executive order for a commission to begin looking at researchers' recommendations for improving communication and the death certification process, and that a memorial would be built to honor the storm's victims.

Multiple estimates

CNN and other news organizations have been raising questions about the official Maria death toll for months. In November, CNN reporters surveyed 112 funeral homes across the island, about half the total. Reporters found that funeral home directors identified 499 deaths they considered to be hurricane-related. In December, The New York Times estimated 1,052 "excess deaths" occurred after Maria. Others produced similar estimates.

A research letter published this month in the medical journal JAMA estimated that between 1,006 and 1,272 people died in connection to the storm.

In May, a team that included researchers from Harvard University published a study in the New England Journal of Medicine estimating that 793 to 8,498 people died in Maria's wake, a range that some academics have criticized as overly broad. The study's midpoint estimate -- 4,645 deaths -- became a rallying cry for activists upset by what they see as a lack of accountability for the scale of the catastrophe by officials in Puerto Rico and the United States.

This year, CNN and the Centro de Periodismo Investigativo, or CPI, in Puerto Rico sued the island's Demographic Registry to make public a database with information about everyone who died in the months after the storm.

Using the same database, CNN reported on deaths labeled in government records as hurricane-related that were not counted by officials; and, in partnership with CPI, reported on an apparent leptospirosis "outbreak" that was not identified as an outbreak by authorities.

The network also created an online database the public can use to search for the names of all the people who died in the months after the storm -- and tell reporters about deaths that may have been related to Maria.